# SU(2) chiral perturbation theory for K(l3) decay amplitudes

Flynn, J.M and Sachrajda, C.T. (2008) SU(2) chiral perturbation theory for K(l3) decay amplitudes. Pre-print, 20pp. (arXiv:0809.1229v1). (Submitted).

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Original Publication URL: http://arxiv.org/abs/0809.1229

## Description/Abstract

We use one-loop \SU(2)_L\times \SU(2)_R chiral perturbation theory (\SU(2) ChPT) to study the behaviour of the form-factors for semileptonic K\to\pi decays with the pion mass at q^2=0 and at q^2_{\textrm{max}}=(m_K-m_\pi)^2, where q is the momentum transfer. At q^2=0, the final-state pion has an energy of approximately m_K/2 (for m_K\gg m_\pi) and so is not soft, nevertheless it is possible to compute the chiral logarithms, i.e. the corrections of O(m_\pi^2\log(m_\pi^2)). We envisage that our results at q^2=0 will be useful in extrapolating lattice QCD results to physical masses. A consequence of the Callan-Treiman relation is that in the \$\SU(2) chiral limit (m_u=m_d=0), the scalar form factor f^0 at \qsqmax is equal to f^{(K)}/f, the ratio of the kaon and pion leptonic decay constants in the chiral limit. Lattice results for the scalar form factor at \qsqmax are obtained with excellent precision, but at the masses at which the simulations are performed the results are about 25% below f^{(K)}/f and are increasing only very slowly. We investigate the chiral behaviour of f^0(\qsqmax) and find large corrections which provide a semi-quantitative explanation of the difference between the lattice results and f^{(K)}/f. We stress the generality of the relation f^0_{P\to\pi}(\qsqmax)=f^{(P)}/f in the \SU(2) chiral limit, where P=K,D or B and briefly comment on the potential value of using this theorem in obtaining physical results from lattice simulations.

Item Type: Article Report number: SHEP-08-26 http://arxiv.org/abs/0809.1229 Q Science > QC Physics University Structure - Pre August 2011 > School of Physics and Astronomy > Southampton High Energy Physics 64183 09 Jan 2009 27 Mar 2014 18:45 http://eprints.soton.ac.uk/id/eprint/64183